derivative of ln(x+1/(ln(x)))

Lösung

\frac{d}{d x} (ln (x) + \frac{1}{ln ( x )})

\frac{1}{x} - \frac{1}{x ln ^{2} ( x )}

Schritte zur Lösung

\frac{d}{d x} (ln (x) + \frac{1}{ln ( x )})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (ln (x)) + \frac{d}{d x} (\frac{1}{ln ( x )})

\frac{d}{d x} (ln (x)) = \frac{1}{x}

\frac{d}{d x} (\frac{1}{ln ( x )}) = - \frac{1}{x ln ^{2} ( x )}

= \frac{1}{x} - \frac{1}{x ln ^{2} ( x )}

\frac{\partial}{\partial x} (x e^{x^{2} y^{2}})

in v erse l a pl a ce \frac{1}{s ( s ^{2} + 6 s + 13 )}

x \to 1 lim (10 x + 15)

\int (\frac{x ^{2}}{4} + 2 x + 3) d x

\frac{d}{d x} (\frac{ln ( 6 x )}{6 x})